Number theory · Greatest common divisor · Divisibility · Squares modulo 5
For a natural number \(n\), determine the greatest common divisor of the two numbers
\[ n^{2} + 1 \qquad \text{and} \qquad (n+1)^{2} + 1 , \]
expressed in terms of \(n\).
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Serbian Regional Competition 2007, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source